The measurable list chromatic number of a graph G is the smallest number such that if each vertex v of G is assigned a set L(v) of measure in a fixed atomless measure space, the...
A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of...
d Abstract) Pascal Ochem∗, Alexandre Pinlou† LaBRI, Université Bordeaux 1, 351, Cours de la Libération, 33405 Talence Cedex, France March 16, 2007 A homomorphism from an ori...
The sum of a coloring is the sum of the colors assigned to the vertices (assuming that the colors are positive integers). The sum (G) of graph G is the smallest sum that can be ach...
We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...